stat4652S23Hwk1

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University of Nevada, Reno *

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452

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Statistics

Date

May 10, 2024

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docx

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1

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STAT 4/652 SPRING 2023 Homework 1 Due on Canvas Thursday, Feb 2 Instructions: 1. Please type your answers. Use full sentences. 2. Please be concise and to the point. No more than 2-3 sentences per question. 3. The total submitted solution can not take more than one page . 4. Each part of the question is worth 5 points. Total for this homework is 15 points. Please consider the following scenario: A study was conducted to determine if a new medicine (NM) is effective in fighting breast cancer. Research team selected at random a group of women with breast cancer and administered the new medicine. After 2 months, results were collected. The goal was to check if the very expensive NM is significantly better than the cheaper and working old medicine. The hypotheses the medical team tested were as follows: Ho : The NM works the same as the old one versus Ha : The NM works better than the old one Answer the following questions: Please note that the answer to question 3 is an opinion, so there is no wrong answer, as long as it is somehow justified. 1. Describe in words the Type I error and Type II error in terms of these hypotheses. In this case a Type I error would consist of the scenario that the NM truly works the same as the old one, but the hypothesis is rejected in favor of the hypothesis that the NM works better than the old. A Type II error would consist of the scenario that the null hypothesis that the NM works the same as the old one is decided to be true but is actually false. 2. Think of the consequences of these errors. Please describe them in words, one sentence for each error. Because a Type I error will bring on a false positive, the primary consequences of this error would be to wrongfully believe that the hypothesis testing was correct when in fact it was not. The consequences of a Type II error would be more of an error of omission, like in the case where a patient is tested for a disease and the results come back negative when in reality they are in fact infected. 3. Does the strategy to keep the chances of Type I error low make sense in terms of the health of the patient? Yes, the strategy to keep the chances of Type I error low makes sense in terms of the health of a patient due to the scenario in which it is concluded that a treatment does have an effect on patient condition, when in reality it has no effect. Due to this scenario in which a form of treatment is concluded to be effective when it is not, it is more beneficial for the patient to risk the chance that a Type II error occurs while minimizing the chance of a Type I error.
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